The motivation of our work in this paper comes from two aspects. The first one is Hu [1]}, in which a global maximum principle for optimal control problem with recursive utilities has been obtained completely. The second one is Song et al. [2]}, in which a new global maximum principle for stochastic control problem of SDEPs, where the control variable enters into both the coefficients of diffusion and jump, has been derived by using a novel spike variation technique, which modifies a critical incorrectness in Tang and Li [3]}, which has been pointed out in the book of Situ [4]} for over sixteen years. Combining the two aspects above with the partially observed feature, in this paper, we aim to study a global maximum principle for partially observed controlled forward-backward stochastic system with random jumps, where all the coefficients contain the control variable. We note that, very recently, Hao and Meng [5]} obtained a global maximum principle for optimal control of the general mean-field forward-backward stochastic system with jumps. However, the jump term in the SDEP of their paper does not contain the control variable and the cost functional is a special recursive case.
